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A better description of driving conditions would help. The torque converter locks up in limited conditions, so if it's happening while the torque converter is not locked up, that would presumably rule out torque converter shudder. Curiously, the OP describes a rumble strip "sound" rather than a rumble strip "feel", and the stuff I've read suggested one would get the latter from torque converter shudder.

I don't know much about A/C stuff, but as I understand it, the A/C compressor cycles on and off repeatedly when it's being used. If the sound always happens when the A/C cycles on, that would seem to suggest some kind of compressor issue, as if the compressor is having a hard time rotating when the clutch first engages. If the sound only happens when the A/C cycles on while the torque converter is locked up, or when the torque converter locks up when the A/C is already cycled on, that could suggest a curious bit of torque converter shudder related to the load of the A/C compressor.

it doesn't cycle that fast. The system cuts out around 25 psi and back in around 45. It takes a couple seconds for that to happen. The shudder I've felt is a whole lot more like a rumble strip. AC cycling is a surge every second or so as the clutch kicks in and out.

It is a 2003 Grand Marquis. The noise does occasionally happen upon first startup but that is the only time it happens when not driving. I cannot replicate the sound from beneath the hood by manually opening and closing the throttle. I have tried a couple of time to have one of my kids start the car with the AC on while I was under the hood but it never seems to do it when I'm under there.

Speed and or RPM doesn't seem to affect whether or not it happens but does seem to affect the intensity of the power loss/speed scrub/ drag and tone(faster/higher sounds more like rumble strips and slower like...slower deeper rumble strips I guess.)

There is some sensation that can be felt but it is more of a sound. When it happens on startup it seems to be coming from under the passenger side of the dash if I had to try to pinpoint the noise from the drivers seat.

Without the AC on it never happens at all and everything functions like a brand new car.

I haven't thought to check with different intensities of ac high vs low because it only worked on high until about a week ago when I fixed the resistor.

Another possibility is that your balancer is going away. My '98 would shudder and make a belt-squeal sound whenever the a/c compressor kicked on. I watched underhood while this was happening and saw the balancer spin on the hub. Just throwing that out there. If you do indeed need a balancer, buy the 4.6 underdrive pulley kit from summit. Costs the same as just a balancer and comes with a fancy SFI balancer, as well as underdrive pullies.

check the belt tension. I have an issue occasionally with my expedition that when the AC compressor engages, the belt tensioner bucks pretty hard keeping the tension on the belt. If the tensioner is getting weak, it could bounce more than that and may sound like a rumble strip. Mine sounds like a once and done speed bump.

check the belt tension. I have an issue occasionally with my expedition that when the AC compressor engages, the belt tensioner bucks pretty hard keeping the tension on the belt. If the tensioner is getting weak, it could bounce more than that and may sound like a rumble strip. Mine sounds like a once and done speed bump.

So in doing this I found the source of the noise though sadly not the cause. I went out and turned on the ac and opened the hood then fired it up and ran around to the front. nothing for a few seconds then rattle goes the tensioner. So I thought great bad tensioner I'll go get that handled done and done. I went to the pick and pull and grabbed one from a 2011 crown vic figuring that one that much newer than mine is more likely still good. No avail still having the same problem. Though I'll admit it is possible that the one I bought is equally bad. Assuming for now that the tensioner rattle is a symptom of the problem and not the problem itself what do you guys think it may be?

Consider the Following:
-only happens when AC is on
-noise caused by vibrating belt tensioner
-has now happened in park and more frequently while driving
-when it happens while driving it scrubs speed and acceleration.

Something like a tensioner is going to be mileage-dependent rather than age-dependent. Someone with a 2011 might very well have driven twice as many miles as someone with a 2003. What's the mileage on your 2003? Do you feel any restriction or slop in the tensioner pulleys? (BTW, RockAuto sometimes has them on clearance for cheap enough to buy a spare.) When was the belt last replaced? [Edit: Did you check all the other pulleys while you had the belt off?]

If everything else is good on the car... you could also use the "crank up the radio" fix. It could just be the sudden shock loading of the clutch engaging on the AC compressor and bounces the tensioner on the belt. There may not be a full fix for that. Like I said... the one on my Expedition does it on first kick but not after that.